ID | 15380 |
JaLCDOI | |
Sort Key | 20
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FullText URL | |
Author |
Morikawa, Yoshitaka
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Abstract | Modern communication engineerings, such as elliptic curve cryptographies, often requires algebra on finite extension field defined by modulus arithmetic with an irreducible polynomial. This paper provides a new method to detemine the minimal (irreducible) polynomial of a given proper element in finite extension field. In the conventional determination method, as we have to solve the simultaneous equations, the computation is very involved. In this paper, the well known "trace" is extended to higher degree traces. Using the new traces, we yield the coefficient formula of the desired minimal polynomial. The new method becomes very simple without solving the simultaneous equations, and about twice faster than the conventional method in computation speed.
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Keywords | finite field
minimal polynomial
irreducible polynomial
higher degree trace
trace
cryptography
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Publication Title |
Memoirs of the Faculty of Engineering, Okayama University
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Published Date | 2001-03-27
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Volume | volume35
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Issue | issue1-2
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Publisher | Faculty of Engineering, Okayama University
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Publisher Alternative | 岡山大学工学部
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Start Page | 197
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End Page | 205
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ISSN | 0475-0071
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NCID | AA10699856
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Content Type |
Departmental Bulletin Paper
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OAI-PMH Set |
岡山大学
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language |
English
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File Version | publisher
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NAID | |
Eprints Journal Name | mfe
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